Numerical study of jet-plate interaction and its effects on aeroacoustics

In modern under-wing-mounted high-bypass engines, the exhausted jet from the engine will interact strongly with the wing and high-lift devices. In this paper, simulations of an isothermal jet flow at Mach number Ma = 0.5 and close to a flat plate are carried out using large-eddy simulation. Far-field acoustic results are obtained via the surface integral method of Ffowcs Williams and Hawkings (FW-H). The studied cases include an isolated jet and other three configurations with the jet and a plate spaced at the distance H/D j = 1.0, 1.5, and 2.0, respectively, from the jet axis. Validation against experimental data is carried out. Far-field acoustic results show that the overall noise levels are significantly increased for the installed cases, particularly for polar angles in upstream of the nozzle. The noise levels are increased more as the plate approaches the jet axis, indicating the installation effect is related to the H/D and the polar angle. The pressure fluctuations are shown to decay along the radial direction. The mean flow and power spectral density of the axial velocity show the characteristics of the jet flow is not significantly changed by the presence of the plate.


Introduction
The rapid development of the civil air transport industry has led to a continuous increase in the number of civil airplanes and airports in service [1].This has resulted in significant noise pollution for airport staff and residents living nearby.Aircraft noise is mainly divided into airframe noise and engine noise.Engine noise is mainly composed of fan noise and jet noise.In modern aircraft, the application of high bypass ratio turbofan engine has reduced the jet noise greatly, but the jet noise still accounts for about half of the total noise when the aircraft takes off [2].
Since Lighthill proposed the acoustic analogy theory in 1952 [3], a large number of studies on the jet and its noise has been conducted.The acoustic analogy of Lighthill was further developed theoretically by Lilley [4].Ffowcs Williams et al. [5] carried out a large number of experiments, confirming the eighth-power law.Before the 1980s, most of the studies on jets were focused on isolated jets.However, high/ultra-high bypass ratio engines are widely used in modern aircraft.In order to meet the minimum installation height above the ground, underwing-installed engines must be more tightly attached to the wing.Therefore, a strong interaction between the jet flow and the wing will appear.The existence of the wing can deflect the jet flow at a certain angle, causing additional noise.Therefore, the current research on the installed jet mainly focuses on its flow field and sound field.
In terms of flow field, Pastouchenko et al. [6] investigated the jet flow of the double-duct installation numerically using the Reynolds Average Navier-Stokes (RANS) method.It was found that the axial velocity distribution cloud at the nozzle exit was almost circular and it was considered that the jet flow was not affected by the wing.Bondarenko et al. [7] conducted a study of the jet-wing interaction numerically using a high-order finite difference LES codes.It was found that the interaction between the jet flow and the wing caused a low-pressure area under the wing and the jet flow was deflected by a small angle towards the wing.Therefore, the influence of wing and high-lift device on jet still needs to be studied furtherly.
In terms of sound field, Curle [8] theoretically solved the problem involving the interaction between flow noise and solid boundaries.Curle's analogy was a generalization of the acoustic analogy of Lighthill.The noise source included the contributions from the forces due to the impact of sound waves produced by quadrupoles on the plate and the flow itself.It was shown that this sound production mechanism is equal to the distribution of a dipole source, representing the fluctuating forces exerted by solid boundary on fluid.Bushell [9] firstly found that noise produced by an installed engine was larger than that of an isolated engine.The influence of the installation effect on the jet noise gradually entered researchers' vision and this condition was named as installation jet.Southern et al. [10] conducted experimental studies on the installed jet under the wing.They thought that the increase of noise in high-frequency came from the reflection of jet noise at the bottom of the wing and there was a low-frequency noise source between the jet and the wing.
To simplify the study of installed jets, Lawrence [11] investigated the feasibility of replacing wing with a flat plate and both of the noise results were very close.Cavalieri et al. [12] conducted research on installation jet by simplified the wing to a flat plate.The results showed that far-field noise was significantly enhanced at low frequencies, and there was a large difference between the reflective side (without flat side) and the shielded side (with flat side).The studies above mainly focused on the comparison of noise between the reflective side and the shielding side of the flat plate.They did not analyse the angle of noise radiation direction on the reflective side, which mainly affect human beings.In this paper, the wing is simplified to a flat plate.Simulations of an isothermal jet flow close to a flat plate are carried out using large-eddy simulation.The studied cases include an isolated jet and other three configurations with the jet and a plate spaced at the distance H/Dj = 1.0, 1.5, and 2.0 from the jet axis.The flow field and sound field under the four conditions are studied.The effects of a plate on the jet flow were obtained by comparison, revealing the effects of the radial distance of the plate on the jet flow field and sound field preliminary.

Models and meshing
This study object is a round, convergent nozzle with an exit diameter Dj = 50 mm.Flow conditions, characterized by subsonic jets with acoustic Mach number × × and the length of nozzle is 4.9 Dj.For installed jets, radial position is defined as the distance of the plate lower surface with respect to the jet centerline.The length of plate, which corresponds to the distance from the nozzle exit plane to the trailing edge, is defined as L =6 Dj.The plate has a thickness t = 0.2 Dj.To avoid scattering effects at the leading edge, it also extends 2 Dj upstream of the nozzle exit plane.In the spanwise direction, the plate has a width of 10 Dj to avoid side-edge scattering.A structured mesh is used for meshing while the mesh near the jet shear layer area and the plate is encrypted.The number of mesh nodes is 4.5×10 6 .

Numerical method
The density-based solver of Fluent is selected for calculation.The diffusion term and convection term are used in central difference and advanced upwind style respectively.The implicit format of secondorder precision is used on time-advancing.The Reynolds Average Navier-Stokes (RANS) method is used to obtain initial flow field while the large eddy simulation is used in the latter calculation.In latter calculation, vortex ring disturbance is added downstream of the nozzle by Fluent UDF compiler and the subgrid model is the Smagorinsky-Lilly model.The dimensionless time advance step is 0.05 Dj /Uj, ensuring CFL number is less than 1 in whole calculation domain.After a period of 400 Dj /Uj, the effects of the initial flow field has been excluded in the calculation domain.Then, turbulence sampling statistics were carried out and the time of statistical sampling lasted for 300 Dj /Uj.The surface integral method of Ffowcs Williams and Hawkings (FW-H) is used to calculate far-field noise.Mendez et al. [13] proposed that most of the energy-containing structures must be contained inside the sound source surface when using the FW-H method.Thangaraj et al. [14] found that the velocity of 30 Dj downstream from the nozzle outlet is close to 0 in subsonic jet.Considering the vortex crosssectional distribution of the jet near-field and including the plate, the FW-H surface is a closed area surface with a length of 30 Dj and a radius of 5 Dj.The monitoring points are located at the concentric circle surface of r = 41 Dj and the center of the circle is the coordinate origin.The monitoring angle θ is the angle with the jet flow direction.The position of the FW-H surface is shown in Figure 1.

Boundary conditions and disturbances
The boundary conditions of all cases are as follows: the inlet boundary condition is a total temperature of 302.4 K and a total pressure of 126103.6Pa, the outlet boundary condition is static pressure, the surfaces of solid wall are insulated without slip and far-field static pressure inlet conditions are given for all other boundaries.Static flow parameters, ambient pressure p ∞ = 101300 Pa and ambient temperature T ∞ = 288 K, are chosen for the computations.In order to quickly transform the jet into turbulence, vortex ring disturbance is added to the velocity distribution of the shear layer area downstream of the nozzle [15].It has circumferential multimodal characteristics, divergence free and low amplitude, which are convenient to numerical calculations and predict jet noise accurately.It modifies the axial and radial velocities every time step in the following way: ' ' cos( )  x r x x r r ∆ = − + − , Δy is the transverse grid spacing.

Numerical validation
To verify the accuracy of the numerical simulation in this paper, the flow and sound results obtained from numerical simulation are compared with that of experiment.To express conveniently, the provisions are as follows: u and u′ represent axial velocity and its fluctuation respectively, a represents the mean value.Figure 2 is streamwise velocity at the jet centerline and lipline.To evaluate the quality of numerical simulation, experimental measurements from reference [16].andresults of large eddy simulation from reference [17] are used for comparison.The results presented in Figure 2(a) indicate that the numerical results at the jet centerline are in good agreement with the experimental measurements and are closer to experimental measurements compared results with from reference [17].The jet potential core length is an important indicator of the jet flow.The jet potential core length from numerical simulation is Lc/Dj=7.2, while the experimental value is Lc/Dj=6.8.
From Figure 2(b), the mean axial velocity at the lipline is lower than experimental value near the nozzle outlet, which is similar with results with from reference [17].However, the results of numerical simulation are in good agreement with experimental values in the downstream.This is because the propagation of disturbances needs certain space.From results above, the numerical model used in this paper is reliable to accurately calculate jet flow fields.The calculation method and boundary conditions used are reasonable and effective.3 compares the simulated OASPL results to experimental measurements from reference [17].From Figure 3, the simulated OASPL level is higher than experimental measurements, and the maximum difference is 3.3dB.This is related to the addition of vortex ring disturbances, which slightly increases the intensity of turbulence.Thus, the radiated noise is increased slightly.A similar phenomenon is observed in reference [15].To Sum up, using the surface integral method of Ffowcs Williams and Hawkings (FW-H) provides a valid prediction of the jet's acoustic.

Mean flow
Analysis of the mean field are carried out to discern if the presence of the plate causes a deformation of the mean field of the jet.With wave packets in jets depending on the turbulent mean flow, it is important to determine if mean velocities are significantly modified by the presence of plate and the proximity of plate to the jet. Figure 4 presents contours of the jet mean flow field under different configurations.Figure 4 indicates that plate has slight impact on the jet mean flow field.In the configuration of H/Dj = 1.0, a small part of the plate trailing edge interacts with the mean velocity flow, changing the mean velocity field nearby.In addition, the plate has a certain influence on the average flow field of the jet in the range of x/Dj = 15~20.In order to quantify whether the plate changes the jet flow, quantitative analyses are made in Figure 5, where a comparison of the mean flow at the jet centerline and lipline is shown for the different configurations.From Figure 5, apart from mean velocity having a small increasing at jet lipline near the plate trailing edge, there are no significant changes in the mean velocity.The jet potential core length under different configurations is shown in Table 1.The presence of the plate increases jet potential core length slightly.As the plate closer to the jet, the jet potential core length increases more.From Figure 6(a), only in the configuration of H/Dj =1.0, the mean velocity near the plate was increased.The mean flow field is changed slightly.From Figure 6(b), the mean velocity of configuration H/Dj =1.0 is higher than others, indicating that the presence of the plate prevents the jet from diffusion in the radial direction and transfers the diffusion along the radial direction to the downstream direction, resulting in velocity increasing in downstream.However, because diffusion of the jet is slow, the velocity increasing is very small.

Streamwise velocity power spectrum
In addition to the mean flow, streamwise velocity power spectrum is used to verify if the plate changes the turbulent structures of the jet flow.Figure 7 investigates the changes on the transient flow field of the jet for different configurations.The figure demonstrates that the velocity power spectrum at the centerline and lipline exhibit different patterns of evolution.At the centerline, there is a noticeable peak around St=0.7, which is close to the theoretical value of 0.68 for instability.For the lipline, it keeps almost stable level, presenting a broadband behavior.Figure 8 and Figure 9 evaluate the impact of the plate on the downstream evolution of the velocity fluctuations at the jet centerline and lipline for a few chosen Strouhal numbers.For the centerline, the power spectrum levels are related to the axial distance.It grows to a stagnation point and remains at an almost constant level, and the position of the stagnant point is related to the Strouhal number.For the lipline, the power spectrum shows almost constant levels for the entire axial range, and there was no apparent dependence on the Strouhal number.The investigation on the jet's mean flow field and streamwise velocity power spectrum made showed that the plate does not change the jet flow significantly for the configurations in this paper.

Pressure field
There are two regimes of the pressure field generated by a jet flow, one is a non-propagating near-field and the other is an acoustic regime that propagates to the far-field.In the near-field, there are two different hydrodynamic sub-regimes, one is a non-linear, rotational hydrodynamic regime and the other is a linear, irrotational hydrodynamic regime [18].Savell [19] studied the relationship between the sound pressure level of the jet and the radial distance.He found that when sufficiently far away from the jet, the intensity of the pressure fluctuation is inversely proportional to the square of the distance, which is consistent with the characteristics of far-field acoustics.He thought that the transition between hydrodynamic, near-field, and acoustic far-field can be determined from the decay rate of pressure fluctuations with the radial distance.
Figure 10 presents the radial evolution of pressure fluctuations in different configurations for some Strouhal numbers.The results are obtained at the axial positions x = 6 Dj.From Figure 10, the pressure fluctuations of low Strouhal numbers decay exponentially at y/ Dj = 1.0 ~ 2.0.It indicates that the plate is interacting with a linear, irrotational hydrodynamic regime.With the increase of radial distance, the decay rate of pressure-field is changed from an exponential decay to an algebraic decay.It is able to observe the scattering of the jet near-field by the plate.For St=0.2, the scattering of the near-field can be observed in all installation configurations, indicating that the wave length of the noise source is very close to the characteristic length of the plate.As the Strouhal number increases, the scattering phenomenon of the configuration with a long radial distance of the plate installation gradually disappears.This suggests that the scattering effect is influenced by the radial distance of the plate installation.When the Strouhal number reaches 1.0, scattering effects cannot be observed in any of the configurations.It indicates that the wavelength of the noise source is much smaller than the characteristic length of the plate.The main mechanism of installation noise is transformed from scattering of hydrodynamic fields to reflection of sound waves.Although the absolute OASPL is slightly higher than the experimental measurement, its relative OASPL is in good agreement with the experiment.Figure 11(a) shows that the overall levels are significantly increased for the installed cases.As the plate closer to the jet centerline, the higher OASPL level.For configuration of H/Dj =1.0, the OASPL levels are almost same for all monitoring angles.Figure 11(b) shows that the OASPL level increases more significantly at the polar angle upstream the nozzle (240°).For configuration of H/Dj =1.5 and 2.0, the increase of OASPL at the polar angle downstream the nozzle (330°) is almost zero.However, there is a 3dB increase at the polar angle downstream the nozzle (330°) for configuration of H/Dj =1.0.It indicates that the increase of the OAPL level at the polar angle downstream the nozzle is related to the installation configuration.The contribution of the installation effect to the OASPL level at the polar angles downstream cannot be ignored.

Spectral characteristics
In order to further study the influence of different installation configurations of plates on jet noise, four angles of 240°, 270°, 300° and 330° are selected for spectral characteristic analysis.Figure 12 shows that SPL (Sound Pressure Level) spectrogram of at different polar angles.It can be seen from the Figure 12 that the increment of SPL level is enhanced and covers a wider range of Strouhal numbers as the plate approaching to the centerline of the jet.This is related to the near-field interaction of the jet with the plate, resulting in noise increasing in the low Strouhal number.In addition, it can be seen that the jet-plate interaction effect is more significant at the polar angle upstream the nozzle by comparing with different polar angles.This is consistent with the high level of OASPL value-added at the polar angle upstream, proving that low-frequency noise is dominant in subsonic jet.

Conclusions
Aimed at interactions between the exhausted jet flow of engine and the surface of the wing, three installation heights are tested to evaluate the installation effects on the jet flow, pressure and sound fields.The following conclusions are obtained: (1) Comparisons of mean streamwise velocity field and streamwise velocity power spectrum shows that the presence of plate does not significantly change the jet flow field for the three chosen installation configurations.
(2) It was found that the pressure fluctuation decay radially and the plate is located in the region that pressure fluctuations decay exponentially.
(3) The sound field of isolated jets and three different installation configurations are studied.As the plate approaching the centerline of the jet, the noise level increases greater and noise at the polar angle upstream increases significantly.It indicates that the installation effect is related to the distance of the plate from the centerline and the polar angle.
. The calculation domain is shown in Figure1.The Cartesian coordinate system is defined with the center of the jet outlet as the coordinate origin.The total size of the calculation domain is

Figure 2 .
Figure 2. Streamwise velocity distribution: (a) centerline and (b) lipline Figure3compares the simulated OASPL results to experimental measurements from reference[17].From Figure3, the simulated OASPL level is higher than experimental measurements, and the maximum difference is 3.3dB.This is related to the addition of vortex ring disturbances, which slightly increases the intensity of turbulence.Thus, the radiated noise is increased slightly.A similar phenomenon is observed in reference[15].To Sum up, using the surface integral method of Ffowcs Williams and Hawkings (FW-H) provides a valid prediction of the jet's acoustic.

Figure 3 .
Figure 3.Comparison of the simulated OASPL results with experimental measurement

Figure 4 .
Figure 4. Streamwise velocity field for different configurations: (a) Isolated jet, (b) Installed jet: H =1.0Dj, (c) Installed jet: H =1.5Dj, and (d) Installed jet: H =2.0DjIn order to quantify whether the plate changes the jet flow, quantitative analyses are made in Figure5, where a comparison of the mean flow at the jet centerline and lipline is shown for the different configurations.From Figure5, apart from mean velocity having a small increasing at jet lipline near the plate trailing edge, there are no significant changes in the mean velocity.The jet potential core length under different configurations is shown in Table1.The presence of the plate increases jet potential core length slightly.As the plate closer to the jet, the jet potential core length increases more.

Figure 5 .
Figure 5. Computational results of streamwise mean velocity: (a) centerline and (b) lipline Table 1.The jet potential core length under different configurations Case Lc/Dj isolated 7.20 H/Dj = 1.0 7.41 H/Dj = 1.5 7.33 H/Dj = 2.0 7.29 Comparing radial distribution of streamwise mean velocity of different configurations can provide a better analysis of the installation effect on the jet mean flow field more visually.Due to the jet potential core length is about 7 Dj and the length of plate is 6 Dj, axial positions x = 6 Dj and x = 8 Dj are chosen to compare radial distribution of streamwise mean velocity, which are shown in Figure 6.From Figure6(a), only in the configuration of H/Dj =1.0, the mean velocity near the plate was increased.The mean flow field is changed slightly.From Figure6(b), the mean velocity of configuration H/Dj =1.0 is higher than others, indicating that the presence of the plate prevents the jet from diffusion in the radial direction and transfers the diffusion along the radial direction to the downstream direction, resulting in velocity increasing in downstream.However, because diffusion of the jet is slow, the velocity increasing is very small.

Figure 7 .
Figure 7. Streamwise velocity power spectrum at axial positions x = 6 Dj: (a) centerline and (b) liplineFigure8and Figure9evaluate the impact of the plate on the downstream evolution of the velocity fluctuations at the jet centerline and lipline for a few chosen Strouhal numbers.For the centerline, the power spectrum levels are related to the axial distance.It grows to a stagnation point and remains at an almost constant level, and the position of the stagnant point is related to the Strouhal number.For the lipline, the power spectrum shows almost constant levels for the entire axial range, and there was no apparent dependence on the Strouhal number.

Figure 11 .
Figure 11.OASPL results at different polar angle: (a) absolute and (b) relative